RISK, RETURN, AND CAPITAL PRICING
MODEL
Summary
Portfolio Theories
Summary:
Risk
●​
Uncertainty in earning.
Return
●​
Gain
or
investment.
over
an
CAPM
●​
Relationship
between
expected return and risk.
the
loss
Return
●​ Total gain or loss experienced on an
investment over a given period of
time.
Markowitz
Portfolio
Theory
(MPT)
●​
Capital Asset
Pricing
Model
(CAPM)
●​
𝐸𝑛𝑑𝑖𝑛𝑔 𝑉𝑎𝑙𝑢𝑒 + 𝐶𝑎𝑠ℎ 𝐹𝑙𝑜𝑤𝑠
𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝑉𝑎𝑙𝑢𝑒
𝐻𝑃𝑌 = 𝐻𝑃𝑅 − 1
𝐴𝑛𝑛𝑢𝑎𝑙 𝐻𝑃𝑌 = 𝐴𝑛𝑛𝑢𝑎𝑙 𝐻𝑃𝑅 − 1
Where;
Annual HPR = HPR1/n
n = investment period (in years)
Risk
●​ Uncertainty that an investment will
earn its expected rate of return.
Accounting for Risk
Risk
Assessment
●​
●​
Sensitivity Analysis – Range
Probability
Distribution
(graph)
Risk
Measurement
●​
●​
Standard Deviation
Coefficient of Variation
Risk Assessment – Range
𝑅𝑎𝑛𝑔𝑒 = |𝑂𝑝𝑡𝑖𝑚𝑖𝑠𝑡𝑖𝑐 𝐶𝑎𝑠𝑒 − 𝑃𝑒𝑠𝑠𝑖𝑚𝑖𝑠𝑡𝑖𝑐 𝐶𝑎𝑠𝑒|
Risk Measurement – SD
𝑆𝐷 =
(𝑘𝑗 − 𝐾)
Risk Measurement – CV
σ
2
●​
Considers the risk-free asset
and ties risk and return.
Developed in the 1960s by
individuals
who
worked
independently.
Limitations:
●​ Some
assumptions
are
unrealistic.
●​ Some variables are unclear
“pixies”.
●​ Systematic risk is unspecified.
Formula:
𝐻𝑃𝑅 =
●​
Developed
the
portfolio
selection article (1952).
Covered the concepts of:
○​ Efficient frontier
○​ Return (represented by
mean or expected value)
■​ Risk = variance
■​ Mean = variance
approach
Arbitrage
Pricing
Theory
(APT)
●​
●​
●​
●​
Developed by Stephen Ross.
Has the ability to identify the
systematic risk factors.
Follows a linear model.
Ex: International rate risk,
changes in GDP, inflation, risk
of changing.
Capital Asset Pricing Model (CAPM)
●​ Developed by Sharpe (1964), Linter
(1965), and Mossin (1966).
●​ Uses past data and presupposes
efficient markets.
Attributes of an Efficient Market
●​ A lot of investors with identical
information and assumptions about
securities.
●​ Free from limitations with regard to
investment, taxes, and transaction
costs.
●​ Sensible inventors.
Kinds of Risk
1.​ Nondiversifiable
risk/systematic
risk/market risk/beta coefficient
2.​ Diversifiable risk/unsystematic risk
𝐶𝑉 = 𝐾𝑘
Page 1 of 9
Total Security Risk
𝑁𝑜𝑛𝑑𝑖𝑣𝑒𝑟𝑠𝑖𝑓𝑖𝑎𝑏𝑙𝑒 𝑅𝑖𝑠𝑘 + 𝐷𝑖𝑣𝑒𝑟𝑠𝑖𝑓𝑖𝑎𝑏𝑙𝑒 𝑅𝑖𝑠𝑘
CAPM Key Notes:
●​ Change in inflation means a new
required return.
●​ Change in risk aversion means a new
required return.
CAPM Assumptions
●​ Limitless funds may be obtained by
investors.
●​ Investors use identical time horizons.
●​ Investors
assess
investment
opportunities by using the portfolio
returns’ expected value and standard
deviations.
●​ Investors project the same probability
distributions for rates of return.
●​ All
assets
are
perfectly
divisible–possible to buy fractional
shares of any asset or portfolio.
●​ Investments
are
free
from
taxes/transaction costs.
●​ The market demonstrates efficiency.
Critiques of the CAPM
●​ Unclear proxy for RF.
●​ Unclear km.
●​ The beta of individual securities may
fluctuate as time goes by.
○​ Thus, use portfolio beta bp
instead of the individual
security’s beta bj.
Formula
𝑘𝑝 = 𝑅𝐹 + [𝑏𝑝 * (𝑘𝑚 − 𝑅𝐹)]
VALUATION
Valuation
●​ Connects risk and return to ascertain
the price of an asset.
Kinds of Value
Book Value
●​
Asset’s value as per the
balance sheet.
Liquidation
Value
●​
How much could an asset be
sold for.
Market Value
●​
The observed value for the
asset in the marketplace.
Intrinsic
(Economic or
Fair) Value
●​
The current value of an
asset’s projected cash flows.
Factors Affecting Value
●​ Size and timing of the projected CFs.
●​ Risk of the projected CFs.
●​ Required return of the investor.
Debt vs Equity Capital
Characteristic
Debt Capital
Equity Capital
Voice in
Management
No (unless
provided)
Yes
Claims on
Income and
Assets
Senior to equity
Subordinate to
debt
Stated
None
Interest
deduction
No deduction
Maturity
Tax Treatment
Bond Valuation
Bond
●​ Long-term debt instrument where a
borrower will pay its holder a fixed
amount of interest annually.
Attributes of Bonds
●​ Claims on assets and income
●​ Par value
●​ Coupon interest rate
●​ Maturity
●​ Indenture
Page 2 of 9
●​ Bond ratings
●​ Current yield
Formula
𝐴𝑛𝑛𝑢𝑎𝑙 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑃𝑎𝑦𝑚𝑒𝑛𝑡
𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑌𝑖𝑒𝑙𝑑 = 𝑀𝑎𝑟𝑘𝑒𝑡 𝑃𝑟𝑖𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝐵𝑜𝑛𝑑
Where:
Annual Interest Payment = Par Value x
Coupon Rate
Types of Bonds
As to Issuer
●​
●​
Government
Corporate
Other Characteristics
●​
●​
●​
●​
●​
●​
●​
●​
Debenture
Subordinated
debenture
Mortgage bonds
Eurobonds
Foreign bonds
Floating-rate bonds
Zero & very low
coupon bonds
Junk
(high-yield)
bonds
International Bonds
●​ Eurobonds:
denominated
in
a
currency other than that of the
country in which they are sold.
●​ Foreign Bonds: sold in a foreign
country and denominated in that
country’s currency.
Philippine Fixed Income Instruments Market
●​ Issuers
are
governments
and
corporations.
●​ Denominated by government issues.
●​ Corporate bonds require a relatively
large minimum investment and are
somewhat illiquid.
●​ Trading is scriptless.
●​ Local credit rating agency – Philippine
Rating Service Corporation.
Fixed Income Instruments Market
●​ Capital Market Infrastructure =
Philippine Dealing System Group
○​ Philippine
Dealing
and
Exchange Corp.
○​ Philippine Depository and
Trust Corp.
○​ PDF Academy and Trust Corp.
Examples of Government-Issued
Income Instruments
●​ T-bills
●​ Zero-coupon bonds
●​ FXTNs
●​ ROPs
●​ RTBs
Fixed
Basic Valuation Formula
Formula:
𝑉 =
𝐶
𝑛
(1+𝑘)
Valuation Formula
Formula:
𝑉𝑏 =
𝐼
𝑡
(1+𝑘)
+
𝑀
𝑛
(1+𝑘)
or
𝑉𝑏 = [𝐼 * 𝑃𝑉𝐼𝐹𝐴] + [𝑀 * 𝑃𝑉𝐼𝐹]
Where:
( )
1
1
⎤⎤
PVIFA = ⎡⎢ 𝑖 * ⎡⎢1 −
𝑛 ⎥⎥
(1+𝑖) ⎦⎦
⎣
⎣
1
PVIF =
𝑛
(1+𝑖)
Remember:
●​ If the coupon rate is EQUAL to the
required return, the bond is traded at
PAR, where the bond value is the par
value.
●​ If the coupon rate is LESS THAN the
required return, the bond is traded at
PREMIUM, where the bond value is
greater than the par value.
●​ I the coupon rate is GREATER THAN
the required return, the bond is
treated at DISCOUNT, where the
bond value is less than the par value.
Page 3 of 9
Bond Valuation if Interest is Paid More Than
a Year
Formula:
𝑉𝑏 =
𝐼
𝑡
(1+𝑘)
+
𝑀
Stock Valuation
Stocks
●​ Represent an ownership interest in a
firm.
𝑛
(1+𝑘)
Types of Stocks
or
𝑉𝑏 = [𝐼 * 𝑃𝑉𝐼𝐹𝐴] + [𝑀 * 𝑃𝑉𝐼𝐹]
Where:
( )
1
1
⎤⎤
PVIFA = ⎡⎢ 𝑖 * ⎡⎢1 −
𝑛 ⎥⎥
(1+𝑖) ⎦⎦
⎣
⎣
1
PVIF =
𝑛
Preferred
Stock
●​
Has features that are present
in bonds and common stock.
Common Stock
●​
Constitutes ownership in a
firm.
Characteristics:
●​ Claim on assets and income
(residual)
●​ Voting rights
●​ Pre-emptive rights
●​ Limited liability
(1+𝑖)
Expected Rate of Return – Yield to Maturity
●​ The discount rate equates the present
value of the future cash flows
(interest and maturity value) with the
bond's current market price.
Issuing Common Stock
Private
Formula:
𝑉𝑏 =
𝐼
𝑡
(1+𝑘)
+
𝑀
𝑛
(1+𝑘)
●​
●​
Venture Capitalists
Angel Capitalists
or
𝑉𝑏 = [𝐼 * 𝑃𝑉𝐼𝐹𝐴] + [𝑀 * 𝑃𝑉𝐼𝐹]
Where:
( )
1
1
⎤⎤
PVIFA = ⎡⎢ 𝑖 * ⎡⎢1 −
𝑛 ⎥⎥
(1+𝑖) ⎦⎦
⎣
⎣
1
PVIF =
𝑛
(1+𝑖)
Primary Market
●​
●​
●​
Philippine Stock Market
●​ Philippine Stock Exchange, Inc.:
Philippines’ sole stock exchange.
Securities Traded
Common Stock
Important Relationship
1
2
●​
As the interest rate rises, the bond value
falls
●​
●​
●​
Premium - kb < coupon interest
Par - kb = coupon interest
Disocunt - kb > coupon interest
3
●​
Vb approaches the par value as the
maturity date nears.
4
●​
Bonds with longer terms are riskier
compared to bonds with shorter maturities.
Initial Public Offering
Rights Offering
Private Placement
●​
●​
Warrants
Exchange Traded
Fund
Preferred Stock
●​
●​
Philippine Deposit
Receipts
Dollar Denominated
Securities
Factors Affecting Performance
●​ Market capitalization: market price
per share.
●​ Value turnover: transaction value.
●​ Index level: trend of the market.
Ways to Profit
●​ Capital gains
●​ Cash dividend
●​ Property dividend
●​ Stock rights (preemptive rights)
●​ Stock dividend
Page 4 of 9
Indices
●​ PSEi
●​ All shares
●​ Sectoral
●​ Others
●​ Price/Earnings
Approach
(P/E)
Multiple
Formula
𝑉𝑐𝑠 = 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝐸𝑃𝑆 * 𝑃/𝐸 𝑅𝑎𝑡𝑖𝑜
Where:
Annual Interest Payment = Par Value x
Coupon Rate
Kinds of Certificates
Scrip
Certificate
●​
Physical stock certificate.
Street
Certificate
●​
Securities are truly owned by
a client but registered in the
name of a nominee broker to
facilitate transactions.
Selected Valuation Models
●​ Single Holding Period Model
Formula
𝐷
𝑃
𝑉𝑐𝑠 = (1 + 1𝑘 ) + (1 + 1𝑘 )
𝑐𝑠
𝑐𝑠
Where:
𝐷1 = Expected dividends
𝑃1 = Forecasted stock price
𝑘𝑐𝑠 = Required return
●​ Zero-growth Model
Formula
𝐷
𝑉𝑐𝑠 = 𝑘
𝑐𝑠
Where:
𝐷 = Expected dividend of the firm
𝑘𝑐𝑠 = Required return
●​ Constant-growth (Gordon) Model
COST OF CAPITAL
Company Cost of Capital
●​ Refers to the expected return on a
portfolio of all the company’s existing
securities.
Formula for Cost of Capital:
𝑟𝐷𝐷/𝑉 + 𝑟𝐸𝐸/𝑉
Formula for After-tax WACC:
(1 − 𝑇𝑐) 𝑟𝐷 𝐷/𝑉 + 𝑟𝐸 𝐸/𝑉
Where:
D + E = V (at market values)
WACC = Weighted Average Cost of Capital
𝑟𝐸= computed using CAPM
Cost of Capital
●​ The rate of return that a firm must
earn on the projects in which it
invests to maintain the market value
of its stock.
Sources of a Firm’s Capital
1.​ Long-term debt
Formula for Before-tax Cost of Debt
Formula
𝐷1
𝑉𝑐𝑠 = 𝑘 − 𝑔
𝑐𝑠
Where:
𝐷1 = Expected dividend of the firm
𝑘𝑐𝑠 = Required return
𝑔 = Projected growth rate
𝑘𝑑 =
𝐼+
𝑀−𝑁𝑑
𝑛
𝑁𝑑+ 𝑀
2
Where:
I = Interest (Par value x Coupon rate)
M = Par value
𝑁𝑑 = Market value
n = Years
Page 5 of 9
2.​ Common stock
4.​ Compute the Weighted Average Cost
of Capital (WACC) or Weighted
Marginal Cost of Capital (WMCC).
Formula (Constant-growth Model)
𝑘𝑠 =
𝐷 1
+𝑔
𝑃0
*WACC is the expected average future
cost of funds over the long run.
*WMCC is the company’s WACC when
more funds are required.
Formula (CAPM)
𝑘𝑠 = [𝑅𝐹 + [𝑏 * (𝑘𝑚 − 𝑅𝐹)]
5.​ Construct
an
investment
opportunities schedule (IOS).
Where:
𝐷1 = Dividends
𝑃0 = Market price of common stock
g = Forecasted dividend growth rate
𝑅𝐹 = Risk-free rate
𝑏 = beta
𝐾𝑚 = Market return
*IOS ranks investment options in
descending order using internal rate or
return as the basis.
6.​ Decide which projects to accept.
Formula for :
𝑟𝐷𝐷/𝑉 + 𝑟𝐸𝐸/𝑉
3.​ Preferred stock
Formula for After-tax WACC:
Formula
(1 − 𝑇𝑐) 𝑟𝐷 𝐷/𝑉 + 𝑟𝐸 𝐸/𝑉
𝐷
𝑘𝑠 = 𝑁𝑝
𝑃
Where:
D + E = V (at market values)
WACC = Weighted Average Cost of Capital
𝑟𝐸= computed using CAPM
Where:
𝐷𝑝 = Par value * Dividend
𝑁𝑝 = Selling price - Flotation Cost
4.​ Retained earnings
Ranking of Funds (cheapest
expensive):
1.​ LTD
2.​ PS
3.​ CS/retained earnings
4.​ New CS
to
most
Other Considerations:
1.​ Costs are measured after taxes.
2.​ Use of target capital structure.
3.​ Application of net proceeds.
4.​ Floatation costs *costs of underwriting
costs and administrative costs.
Steps in Determining the Cost of Capital
1.​ Calculate the specific costs of capital.
2.​ Determine the breakpoints *level of
total new financing at which the cost of
one of the financing components rises.
CAPITAL BUDGETING TECHNIQUES
Capital Budgeting
●​ Involves evaluating and selecting
long-term
investments
which
maximize the owner’s wealth.
Main Reasons for Capital Expenditures
●​ Expansion
●​ Replacement
●​ Renewal
●​ Others:
○​ Advertising
○​ Research and Development
○​ Management Consulting
○​ New Products
Kinds of Projects
Independent
●​
Cash flows are unrelated.
Mutually
Exclusive
●​
Investments that compete with
one another.
3.​ Optional: Make a cost schedule.
Page 6 of 9
Types of Cash Flows
Conventional
Cash Flow
●​
Initial outflow is followed only
by a series of inflows.
Unconventio
nal Cash
Flow
●​
Initial outflow is followed by a
series of inflows and outflows
*Initial investment and annual free cash
flows are always present in a capital
expenditure project.
*Terminal cash flow may or may not be
present in a capital expenditure project.
of
Capital
Unsophisticated
●​
●​
Formula:
𝑉𝑏 =
Important Cash Flows
●​ Initial outlay or initial investment
●​ Annual free cash flow
●​ Terminal cash flow
Classification
Techniques
Discounted Payback Period
●​ How long will it take to get back the
initial investment from the discounted
free cash flows.
Budgeting
Sophisticated
Book Rate of Return
Payback Period
●​
●​
●​
●​
●​
Discounted Payback
Period
Net Present Value
Profitability Index
Internal Rate of
Return
Modified Internal
Rate of Return *uses
future value
Payback Period
●​ How long will it take to get back the
initial investment.
*The shorter, the better.
𝐼
𝑡
(1+𝑘)
+
𝑀
𝑛
(1+𝑘)
or
𝑉𝑏 = [𝐼 * 𝑃𝑉𝐼𝐹𝐴] + [𝑀 * 𝑃𝑉𝐼𝐹]
Where:
( )
1
1
⎤⎤
PVIFA = ⎡⎢ 𝑖 * ⎡⎢1 −
𝑛 ⎥⎥
(1+𝑖) ⎦⎦
⎣
⎣
1
PVIF =
𝑛
(1+𝑖)
Net Present Value
●​ Present value of the free cash flows
after tax.
○​ Considers the time value of
money;
○​ Relies on forecasted cash
flows and the opportunity
cost of capital; and
○​ May be summed up.
Formula:
𝑉𝑏 =
𝐼
𝑡
(1+𝑘)
+
𝑀
𝑛
(1+𝑘)
or
𝑉𝑏 = [𝐼 * 𝑃𝑉𝐼𝐹𝐴] + [𝑀 * 𝑃𝑉𝐼𝐹]
Where:
( )
1
1
⎤⎤
PVIFA = ⎡⎢ 𝑖 * ⎡⎢1 −
𝑛 ⎥⎥
(1+𝑖) ⎦⎦
⎣
⎣
1
PVIF =
𝑛
(1+𝑖)
Formula:
𝑉𝑏 =
𝐼
𝑡
(1+𝑘)
+
𝑀
𝑛
(1+𝑘)
or
𝑉𝑏 = [𝐼 * 𝑃𝑉𝐼𝐹𝐴] + [𝑀 * 𝑃𝑉𝐼𝐹]
Where:
( )
1
1
⎤⎤
PVIFA = ⎡⎢ 𝑖 * ⎡⎢1 −
𝑛 ⎥⎥
(1+𝑖) ⎦⎦
⎣
⎣
1
PVIF =
𝑛
Profitability Index
●​ Also known as the benefit/cost ratio.
●​ Dividing the present value of FCFs by
the initial investment.
Formula:
𝑉𝑏 =
𝐼
𝑡
(1+𝑘)
+
𝑀
𝑛
(1+𝑘)
or
(1+𝑖)
𝑉𝑏 = [𝐼 * 𝑃𝑉𝐼𝐹𝐴] + [𝑀 * 𝑃𝑉𝐼𝐹]
Page 7 of 9
Where:
( )
1
1
⎤⎤
PVIFA = ⎡⎢ 𝑖 * ⎡⎢1 −
𝑛 ⎥⎥
(1+𝑖) ⎦⎦
⎣
⎣
1
PVIF =
𝑛
(1+𝑖)
Internal Rate of Return
●​ The rate of return a project earns.
●​ Rate where the present value of
inflows is the same as the present
value of outflows.
Add/Less: Taxes on sale of old asset
XXX
Sub-total
XXX
Add/Less: Net working capital
XXX
Initial outlay
XXX
Formula:
𝑉𝑏 =
𝐼
𝑡
(1+𝑘)
+
𝑀
𝑛
(1+𝑘)
or
𝑉𝑏 = [𝐼 * 𝑃𝑉𝐼𝐹𝐴] + [𝑀 * 𝑃𝑉𝐼𝐹]
Where:
( )
1
1
⎤⎤
PVIFA = ⎡⎢ 𝑖 * ⎡⎢1 −
𝑛 ⎥⎥
(1+𝑖) ⎦⎦
⎣
⎣
1
PVIF =
𝑛
(1+𝑖)
Remember:
●​ NPV is preferred over IRR in theory;
however, IRR is preferred over NPV in
practice.
CASH FLOW ESTIMATION
Important Cash Flows
●​ Initial outlay
●​ Annual free cash flows
●​ Terminal cash flow - after-tax
proceeds from selling
Initial Outlay
●​ Also known as the initial investment.
●​ The cash outflow required to acquire
the asset.
Formula:
Cost of the asset
XXX
Add: Incidental expenses
XXX
Installed cost of the asset or depreciable
cost of the asset
XXX
Less: Proceeds from the sale of old asset
XXX
Page 8 of 9
Determining the Operating Cash Flows
●​ Pro Forma Approach
Formula
Earnings before interest and
taxes
XXX
Less: Taxes
XXX
Add: Depreciation
XXX
OCF
XXX
●​ Add Back Approach
Formula
Net income
XXX
Add: Depreciation
XXX
OCF
XXX
●​ Definitional Approach
Formula
^ADDED TO INITIAL INVESTMENT
Revenue
XXX
Less: Cash expenses
XXX
Less: Taxes
XXX
OCF
XXX
^SUBTRACTED TO INITIAL INVESTMENT
Annual Free Cash Flows (FCFs)
●​ Operating cash flows.
●​ Changes in working capital
capital spending.
Formula:
Project’s OCFs
XXX
Less: NWC
XXX
Less: Capital spending
XXX
FCF
XXX
●​
and
Formula
Revenue - Cash expenses
XXX
Multiply: 1 - Tax rate
XXX
Sub-total
XXX
Add: Depreciation * Tax rate
XXX
OCF
XXX
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●​ Depreciation Tax Shield Approach
Terminal Cash Flow
●​ Includes the salvage value of the
project plus or minus any taxable
gains or losses.
Formula:
After-tax salvage value of the project
XXX
Less: Cash outlays associated with the
project’s termination
XXX
Add: Recapture of non-expense outlays
that occurred at the project’s initiation
XXX
TCF
XXX
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